Let S={1,2,3,4}. With respect to the lexicographic order based on the usual less than relation:

a)find all pairs in S x S less than (2,3)

ans: (1,1),(1,2),(1,3),(1,4),(2,1),(2,2)

b) all pairs in S x S greater than (3,1)

ans: (3,2),(3,3),(3,4),(4,1),(4,2),(4,3),(4,4)

c) draw the Hasse Diagram of poset (SxS,≼)

I understand posets and Hasse Diagrams but I am having a hard time visualizing part c.

(The answers to a) and b) are correct.)

The lexicographic order is a total order. As Moo commented, the ordering is

(1,1)<(1,2)<(1,3)<(1,4)<(2,1)<(2,2)<...<(4,3)<(4,4 ).

In a Hasse diagram, you only need to connect each element to its immediate successor. So put all 16 elements in a line, starting with (1,1) and going up to (4,4), and draw a line from each element to its successor.

In a Hasse diagram, you only need to connect each element to its immediate successor. So put all 16 elements in a line, starting with (1,1) and going up to (4,4), and draw a line from each element to its successor.